In A World of States of Affairs(Cambridge University Press, 1997) David Armstrong offers acomprehensive metaphysics based on the thesis that the world consistsof states of affairs. Among the entities postulated by Armstrong's theory are relations, including non-symmetrical relations, and whileArmstrong does not agree with Russell that all relations have adirection or definite order among their places, he does explicitlyacknowledge that the slots of a non-symmetrical relation have adefinite order or direction. I first show that non-symmetricalrelations pose a problem for Armstrong's theory by raising TheProblem of Converse Relations. I then argue that the bestresolution of this problem in the context of Armstrong's theoryinvolves adopting an analysis of the order or direction of a relationthat differs from the analysis that Russell assumes. I conclude bydiscussing a further problem facing Armstrong's ontology: TheProblem of Converse Relational Properties.